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For Teaching Math, Two Ways Are Better Than One

If you think you’re bad at math, you’re not alone. Large percentages of adults lack confidence in their math skills; even teachers have surprisingly low ratings of their ability in the subject. But it might be possible to reverse that trend for our children. Research suggests that one straightforward approach can help students develop a clearer understanding of math: teaching multiple strategies to perform the same skill. When teachers demonstrate two ways to do subtraction or multiply fractions, students are more likely to master the skill, according to research conducted by Jon Star, Bethany Rittle-Johnson, and Kelley Durkin. The researchers have found the approach to be effective in many different classrooms, they explain in a recent article for Policy Insights from the Behavioral and Brain Sciences

Many of us probably remember math classes dominated by reciting multiplication tables and memorizing formulas. But that has been changing in American schools. There is an increasing movement away from rote learning toward developing a deeper understanding of math concepts and the ability to apply them. For example, the Common Core State Standards in Mathematics emphasize students’ ability to explain their thinking and discuss similarities and differences in problem-solving strategies. But on a major national assessment in 2011, less than 60% of eighth graders understood algebra sufficiently to find an equation equivalent to n + 18 = 23.

Star and his colleagues have set out to change that by testing a simple classroom shift: teaching students to use multiple methods for solving the same problem. In a typical study, they ask a group of teachers to show how two fictional students, Alex and Morgan, have solved an algebra problem, each in a different way. The teachers then pose scripted questions like “Even though Alex and Morgan did different first steps, why did they both get the same answer?” and “On a timed test, would you rather use Alex’s way or Morgan’s way? Why?” Across many studies, the researchers have found that discussing these questions and comparing the two methods led the students to learn more than a control group whose teachers used a typical teaching style. The students developed greater “procedural knowledge” (the ability to “execute action sequences to solve problems”) and greater “procedural flexibility” (a set of skills that underlie efficient problem solving, such as choosing the best method to solve new problems).

As with all teaching strategies, however, the success of the method depends on how you do it. The researchers have found that it helps if students have prior knowledge of one of the strategies or if teachers slow down the pace of instruction so there is adequate time to teach both strategies thoroughly. And of course, teachers are more successful when they are trained in how to facilitate the discussions, so the researchers developed a supplemental curriculum and training for it. The results were promising but mixed. On the one hand, students learned more when their teachers used multiple strategies. On the other, the teachers used the approach and materials much less frequently than hoped: 30% used them 5 times or fewer over the entire school year and 18% never used them at all, despite the fact that teachers generally understood how. Change is hard, even when it means changing a teaching approach that many of us found unhelpful in our own schooling.

Star and colleagues hope to integrate their discussion prompts into other existing curricula, to make it easier for teachers to implement. Given the promising results of their research so far, that may be worth it. It may take a concerted effort to make a small change, but that small change appears to have a large pay-off.


Original journal article: Jon R. Star, Bethany Rittle-Johnson, and Kelley Durkin, “Comparison and Explanation of Multiple Strategies: One Example of a Small Step Forward for Improving Mathematics Education

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